kirankp wrote:
Is \((x – 2)^2 > x^2\)?
(1) \(x^2 > x\)
(2) \(\frac{1}{x} > 0\)
Target question: Is (x - 2)² > x²?This is a great candidate for
rephrasing the target question.
Take
(x - 2)² > x² and expand the left side to get:
x² - 4x + 4 > x²Subtract x² from both sides to get:
-4x + 4 > 0Add 4x to both sides to get:
4 > 4xDivide both sides by 4 to get:
1 > x REPHRASED target question: Is x < 1? Aside: the video below has tips on rephrasing the target question Statement 1: x² > x Subtract x from both sides of the inequality to get: x² - x > 0
Factor to get: x(x - 1) > 0
This means that
EITHER x < 0
OR x > 1
So there are two possible cases to consider.
case a: If x < 0, then it
IS the case that x < 1case b: If x > 1, then it
is NOT the case that x < 1Since we cannot answer the
REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: (1/x) > 0 If 1 divided by x equals some POSITIVE value, we can conclude that
x is POSITIVEIf x is POSITIVE, then
x could be greater than 1, or
x could be less than 1Since we cannot answer the
REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined Statement 1 tells us that that
EITHER x < 0
OR x > 1
Statement 2 tells us that x is POSITIVE
So, we can
eliminate the possibility that x < 0
This means it MUST be the case that x > 1
So, we can conclude that
x is NOT less than 1Since we can answer the
REPHRASED target question with certainty, the combined statements are SUFFICIENT
Answer: C
Cheers,
Brent